Redirect page for a custom post type

I don’t think you need a redirect. You are missing the rewrite rule for your custom post type.

register_post_type('cp_clients', array(
    'labels' => array(
        'name' => __('Clients'),
        'singular_name' => __('Client')
    ),
    'public' => true,
    'has_archive' => true,
    'supports' => array('thumbnail', 'title', 'editor')
    'rewrite' => array('slug'=>'companies')
);

You should now be able to create and use single-cp_clients.php, and archive-cp_clients.php template files. And your urls will look like example.com/comapnies and example.com/comapnies/acmecorp